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Article overview
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Bosonic and k-fermionic coherent states for a class of polynomial Weyl-Heisenberg algebras | | Mohammed Daoud
; Maurice R. Kibler
; | | Date: |
21 Oct 2011 | | Abstract: | The aim of this article is to construct ’a la Perelomov and ’a la
Barut-Girardello coherent states for a polynomial Weyl-Heisenberg algebra. This
generalized Weyl-Heisenberg algebra, noted A(x), depends on r real parameters
and is an extension of the one-parameter algebra introduced in Daoud M and
Kibler MR 2010 J. Phys. A: Math. Theor. 43 115303 which covers the cases of the
su(1,1) algebra (for x > 0), the su(2) algebra (for x < 0) and the h(4)
ordinary Weyl-Heisenberg algebra (for x = 0). For finite-dimensional
representations of A(x) and A(x,s), where A(x,s) is a truncation of order s of
A(x) in the sense of Pegg-Barnett, a connection is established with k-fermionic
algebras (or quon algebras). This connection makes it possible to use
generalized Grassmann variables for constructing certain coherent states.
Coherent states of the Perelomov type are derived for infinite-dimensional
representations of A(x) and for finite-dimensional representations of A(x) and
A(x,s) through a Fock-Bargmann analytical approach based on the use of complex
(or bosonic) variables. The same approach is applied for deriving coherent
states of the Barut-Girardello type in the case of infinite-dimensional
representations of A(x). In contrast, the construction of ’a la
Barut-Girardello coherent states for finite-dimensional representations of A(x)
and A(x,s) can be achieved solely at the price to replace complex variables by
generalized Grassmann (or k-fermionic) variables. Some of the results are
applied to su(2), su(1,1) and the harmonic oscillator (in a truncated or not
truncated form). | | Source: | arXiv, 1110.4799 | | Services: | Forum | Review | PDF | Favorites | |
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